Potentiometers

You know potentiometers as the volume control knob on almost any audio
equipment, until recently when they started to go digital. Above is what's
behind the panel, but more interesting is what's inside:

The potentiometer contains a strip of resistive material wrapped almost
all the way around the inside of the body. The ends of the strip are connected
to the two outer terminals. There is a third terminal, in the middle, which
is connected to a wiper. That wiper contacts the curved resistive
strip at some point along its length, which you control by turing the knob.
In the picture above the wiper is pretty close to the left terminal. The
symbol for a potentiometer says it all. (The arrow just represents the
wiper, not a current)

You can think of a potentiometer as two resistors in series. Imagine
separating the resistive strip at the point that the wiper touches it:

Since the end-to-end resistance of the potentiometer is unchanged, reagrdless
of where we physically put the wiper or where we imagine breaking the resistive
strip into two parts, we know that the total resistance between terminals
1 and 2 is a constant, which is called the resistance of the potentiometer,
R, and that the two parts must add up to R:

R = R1 + R2

(1)

As you turn the knob, R1 and R2 change but their
sum remains constant. Let's impose a voltage across terminals 1 and 2,
using a battery. We'll measure the voltage across terminals 1 and 2 (call
it V12) as well as that across terminals 2 and 3 (call it V23)

Remember that no current flows through a voltmeter. To emphasize that,
I've drawn the part of the circuit where current flows black, while the
"measure only" part is red.

In the symbol for battery, the broad side is positive. If the battery
is a 6 volt battery, what does voltmeter V12 read? (Easy question,
but get the sign right)

What is the current i that flows in the circuit? For this you can
treat R1 and R2 as a pair of resistors in series,
or you can treat them as a single resistor R.

Given that the current through R2 is i as you calculated
it above, what is the voltage measured by V23? Use the constitutive
law of R2

When the wiper is moved all the way toward terminal 1, what is V23?
(Ask first, what is R1?)

When the wiper is moved all the way toward terminal 2, what is V23?

When the wiper is half way, what is V23?

Your answers above reflected a constant voltage V12 from a battery.
If V12 had been instead an audio signal from a CD player, and
V23 were the audio signal going into your amplifier, what would
be the effect of turning the knob all the way toward terminal 1? All the
way toward terminal 2?

Given that the knob would be above the body in the picture, and
that we want full-clockwise to be loudest, should we use the left
terminal as terminal 2, or the right terminal? Terminal 2 is called the
common terminal, because it is involved with both the input and
the output.

The configuration of two resistors shown here is called a voltage
divider. This term is usually used when the two resistors are fixed
resistors, not part of a single resistor with a "tap" in the middle as
they are in the case of a potentiometer. You can think of a potentiometer
as an adjustable voltage divider.

Draw a schematic diagram of the circuit below. (You can click on the battery,
the battery holder , or the circuit board to see detail, and you may need
the resistor color code)
Calculate the current running through the three resistors, and then the
voltage across the one that is being measured. What does the voltmeter
read? Note carefully the polarity of the voltmeter.